I think I had trouble with this before. With Onun, does that mean the singer or the song? Why do we need the possessive (or genitive is it)? Sorry.

That points out "her" ,  the song her [she] singing 

The possessive is on the verb, with the participle -dIK  

Onun ---> genitive in pronoun 

The reason behind the using possesive form is  that because the song is sung by her, it is performed by her not somebody else. The action of singing is POSSESSED by HER only.